# Purpose of the program: schools, colleges, universities, research centers

The software program “Wave geometry” is intended for research in the field of acoustics, electrodynamics and quantum mechanics, as well as for demonstration of wave phenomena and processes in simple and complex systems of wave-forming sources. The program provides ample opportunities for the researcher to visualize the studied processes and obtain accurate parametric data.

The program is based on Euclidean geometry, in which an axiom missed by Euclid is added to the known axioms: the axiom which states the presence of a base medium (the axiom of the base). At its core, this is a substrate (carrier) for displaying points, lines, shapes in both “frozen” and kinematic form.

Without a carrier of constructs (base), there is no way to display anything. The carrier can be one-dimensional, two-dimensional, and imaginary. The carrier is always motionless in relation to the external observer and is an absolute frame of reference.

The mathematical tools for the calculation and screen-display are algebraic and trigonometric.

#### What the program will demonstrate:

• Doppler effect (all variants at V=const);
• Doppler effect during acceleration of "source-receiver" system (V=at);
• Doppler effect during accelerated motion of either the source, the receiver, or both;
• the compression of standing waves (length of the base, correction for phase);
• speed of energy transfer;
• interference from two or more sources;
• self-organization of two or more sources;
• reaction of the system of sources to a change in parameters;
• movement and self-movement of flexible systems consisting of two or more sources;
• movement and self-movement of rigid systems consisting of two or more sources;
• distribution of kinetic and potential energy in the source system;
• wave calculator that allows the user to automatically calculate all geometric and wave parameters;
The user will be able to vary the parameters and observe the changes occurring both in the field of interfering waves and with the source system.

#### Doppler effect

• user will be able to study/investigate the Doppler effect for all possible standard situations;
• user will be able to study/investigate the Doppler effect for the situation of system in motion with acceleration;
• user will be able to set and receive data of wavelengths and frequencies of sources and receivers;

#### The compression of standing waves

• user will be able to study and compare the dependence of the standing wave length on the speed and orientation of the source system;

# Builder

This functionality will allow you to construct interferometric devices and visualize the wave processes occurring in the device, as well as to predict the results. In the program, you can select the original postulates that underlie a particular physical model, and compare the results.

For example, the Michelson interferometer.

There are at least two conditions for analysis:

1) Existence of wave medium (luminiferous aether);

2) Absence of wave medium (luminiferous aether);

To study condition #1, three variants of coordinate transformations are selected: according to Galileo, according to Lorentz and according to Voigt. It will be possible to investigate the ballistic version proposed by Walther Ritz.

For option #2, in which the speed of waves is always constant relative to the radiating source, one can also view what is happening.

#### Basic formulas included in the program:

• dependence of the wavelength on the source velocity (Doppler effect);
• dependence of the received frequency on the speed of the source/receiver;
• dependence of the standing wave length of an approaching or receding mirror/source;
• dependence of the standing wave length in the system of oscillating sources on its velocity and orientation angle to the direction of motion;
• dependence of the symmetry of the wave image in a moving system on the reduction of the system’s size and phase shift between the oscillating elements;

# About the engineering component of the program

The program will provide a unique opportunity to study the properties of natural (floating) and artificial (rigid) structures of active elements (wave sources) for certain parameters, as well as changes these parameters and observe the effects.

Importantly, the program has features that allows one to study the illusive property physics terms “inertia” by showing the user an unambiguous visual display of the precise physical processes that give rise to this property. Similarly, inert motion or motion by inertia (acceleration without counter-active forces) can be studied e.g. how does the system, being in an arbitrary speed mode, maintain a state of equilibrium of internal forces?

This feature will allow one to understand how to manage complex systems of active elements in order to get a desired form of movement or reaction in the wave medium (luminiferous aether).